The gluonic contribution tog 1 P (x,Q 2) in the parton model

We present a careful analysis of the polarized photon-gluon fusion process. Discussing various regularization schemes it is demonstrated that one can safely extract a hard gluonic contribution to the proton's spin dependent structure functiong ₁ ^P . The value of the first moment of the gluonic Wilson coefficient is shown to be in agreement with the anomaly result. Furthermore, we examine the question whether the gluonic contribution alone can account for existing experimental data forg ₁ ^P (x,Q ²) (x≧0.01, <Q ²>?Q ₀ ² =10 GeV²) and find a positive answer.     

Estimate of the screening corrections to gluon distributions in the smallx region

The screening corrections to gluon distributions in a proton corresponding to the triple gluonic ladder diagram are estimated. They are found to be relatively small: their values does not exceed 10% of the leading order QCD gluon distribution forx?10^?4 andQ ² ?100 GeV².     

Model for nucleon gluon and sea quark structure functions at allx and allQ 2 from the correspondence between QCD and DTU

We propose a simple parametrization of the nucleon gluon and sea quark structure functions at allx, and allQ ². We use the DTU parton model to fix the parametrization at a reference point (Q ₀ ² =1.25 GeV² andA ²=0.01 GeV²) and we mimic the QCD evolution by replacing the dimensioned parameters of the DTU parton model by functions depending onQ ².     

On the extraction of elastic neutron electromagnetic form factors from highQ 2 D(e,e′) scattering

The problem of extraction of the neutron magnetic form factor from highQ ² D(e, e′) data is considered. We calculate the inelastic contribution to the cross section using two models of the EMC effect and find that the extracted value ofG _Mn(Q ²) is not sensitive to the deuteron structure forQ ²≦6 GeV². At the same time accurate data atQ ²>10 GeV² and x≧ l would enable to establish presence of the EMC type effect for the deuteron.     

Model for nucleon valence structure functions at allx,allp ⊥ and allQ 2 from the correspondence between QCD and DTU

We propose a simple parametrization of the nucleon valence structure functions at allx, allp _⊥ and allQ ². We use the DTU parton model to fix the parametrization at a reference point (Q ₀ ² =3 GeV²) and we mimic the QCD evolution by replacing the dimensioned parameters of the DTU parton model by functions depending onQ ². Excellent agreement is obtained with existing data.     

The structure function of the pion

The data on muon-pair production in pion interactions on a nuclear target are reanalysed in the light of what we know about nucleon structure functions in a nuclear environment. A consistent picture of the pion structure function is obtained, which is compatible with the evolution of a hard valence quark distribution atQ ²=2.5 GeV². Vector dominance is used to estimate the hadronic component of the photon structure function atQ ²=2.5 GeV² and it is found to saturate the data there.     

Gluon distributions in real and virtual photon and the photon structure function

Gluon distributions in real and virtual photons are calculated using evolution equations in the NLO approximation. The quark distributions in the photon determined on the basis of the QCD sum rule approach in [1] are taken as an input. It is shown that gluon distribution in the photon can be reliably determined up tox=0.03÷0.05, much lower than the corresponding values in the case of quark distributions. Two variants of the calculations are considered: (1) it is assumed that there are no intrinsic gluons in the photon at some low normalization pointQ ²=Q ₀ ² ∼1GeV²; (2) it is assumed that gluonic content of the photon at lowQ ₀ ² is described by gluonic content of vector mesonsρ, ω, ϕ. The gluon distributions in these two variants appear to be different. This fact permits one to clarify the origin of nonperturbative gluonic content of the photon by comparing the results with experiment. Structure functionsF ₂(x) for real and virtual photon are calculated and it is shown that in the regionx≥0.2 where QCD approach is valid, there is a good agreement with experiment.     

A measurement of the proton structure function F2(x,Q2)

A measurement of the proton structure function F₂(x, Q²) is reported for momentum transfers squared Q² between 4.5 GeV² and 1600 GeV² and for Bjorken x between 1.8 × 10⁻¹⁴ and 0.13 using data collected by the HERA experiment H1 in 1993. It is observed that F₂ increases significantly with decreasing x, confirming our previous measurement made with one tenth of the data available in this analysis. The Q² dependence is approximately logarithmic over the full kinematic range covered. The subsample of deep inelastic events with a large pseudo-rapidity gap in the hadronic energy flow close to the proton remnant is used to measure the “diffractive” contribution to F₂.     

Analysis of the electroproduction structure functions in the lowQ 2 region,combining the vector meson dominance and the parton model with possible scaling violation

The nucleon structure functionF ₂ is constructed and analysed for low values ofQ ² using the generalised vector meson dominance representation with the largeQ ² spectral function calculated from the analytic continuation of the parton model structure function. Various parametrisations of the parton distributions are considered. Possible effects of the largeQ ² scaling violation on the lowQ ² part of the structure function are investigated. The magnitude of the total contribution given by this asymptotic part can be as high as 50% of the vector meson contribution in the low-Q ², low-χ region. The contribution of the valence quarks alone to the structure function at lowQ ² turns out to be at least as important as the corresponding non-Pomeron Regge-pole-like terms coming from the vector meson part. Increase of the structure function with ν coming from the increase of the quark sea in the limit of small χ implied by QCD turns out to be relatively weak at lowQ ². Predictions of the model are compared with available experimental data. The photoproduction cross section and the nuclear effects in the structure function are also briefly discussed.     

P T andQ 2 dependence of multijet production in γγ* collisions

In the context of a measurement recently performed by the PLUTO Collaboration at PETRA, we have computed the contribution of 2-jet, 3-jet and 4-jet production processes (each involving 2 large-p _T jets) in γγ^* collisions to the differential cross sectiondσ/(dp _T dQ ²), whereQ ² is the γ^*'s four momentum squared. It results that the total correction to the 2-jet contribution \(\left( {\gamma \gamma ^ * \to q\bar q} \right)\) , obtained forp _T andQ ² values located in the range 2 GeV<p _T <6 GeV and 0.1 GeV²<Q ²<12 GeV² varies rather slowly as a function of those two parameters; it ranges between 30% and 70%. The specific contribution of the higher twist term involving the process \(\gamma \gamma ^ * \to Mq\bar q\) appears to be insignificant. The discrepancy observed between experiment and theory atQ ²?0.3 GeV² andp _T ?2-3.5 GeV is not explained by our results.     

Spin physics at HERMES

The primary goal of the HERMES experiment is the study of the spin structure of the nucleon. Results on the measured inclusive and semi-inclusive hadron asymmetries using a polarized positron beam on polarized ³He, hydrogen and deuterium targets are here presented. In the covered kinematic range, 0.023<x _Bj <0.6 and 1 GeV²<Q ²<10GeV² the polarized quark distribution were determined for all up (u+?u) and down (d+?) quarks, and separately for valence and sea quarks. The up quark polarization is positive, and the down quark polarization is negative. The polarization of the sea is consistent with zero in the measured range. A first indication of a positive gluon polarization is presented, based on the measured spin asymmetry in the photo-production of hadron pairs with high transverse momentum p _T . This asymmetry is negative, which is in contrast to the measured positive asymmetry for inclusive experiments.     

On theQ 2-extrapolations of AF-corrected Drell-Yan processes

TheQ ²-dependence of the integrated Drell-Yan cross sections with asymptotic freedom (AF) corrections is investigated forQ ²≦ 10⁷ GeV². Existing AF-parametrizations lead to widely differing predictions. Lowest order QCD indicates a strong dependence on thex-behaviour of the input momentum distributions (atQ ²=Q ₀ ² ) which for sea quarks and gluons are guesses. Consequently, AF-corrected Drell-Yan extrapolations toW-energies and beyond involve considerable uncertainties.     

Radiatively generated parton distributions for high energy collisions

The gluon and antiquark distributions of the nucleon are generated radiatively using the assumption that at some low resolution scale the nucleon consists entirely of valence quarks and valence-like gluons. The agreement between the uniquely predicted gluon and sea distributions and the available data on deep inelastic structure functions (including also recent low-Q ² measurements) and direct-photon production is demonstrated and discussed in detail. Simple parametrizations of the resulting (positive definite!) parton distributions are presented in the range 10^?4?x≦1 and 0.2?Q ²?10⁶ GeV² as obtained according to the leading- and higher-order renormalization group evolution equations.     

On the possibility of measuringF L (x,Q 2) at HERA using radiative events

It is shown that a significant measurement of the longitudinal structure functionF _L (x, Q ²) can be performed at HERA, forQ ²=2 GeV² andQ ²=5 GeV² and forx around 10^?4, using radiative events with hard photon emission collinear to the incident lepton beam, under the present running conditions and with an integrated luminosity of 10 pb^?1. The influence of experimental conditions is discussed.     

Early scaling in two photon reactions?

We show that the interpretation given by the TPC/2γ collaboration that their results for the photon structure functionF ₂ ^γ (x) indicates precocious scaling forQ ²>0.3 GeV² andx<0.1 is questionable. It appears to be a spurious effect possibly due to the fact that (i) the authors do not include two prong events (important at lowW), and (ii) in presenting the data they have averaged theW dependence in eachQ ² bin. To estimate the pointlike contribution of the offshell photon, we use the quark parton model (QPM) and find that this accounts for the data forQ ²>20 GeV² and all values ofW. This hard component is also responsible for the bulk of the cross section at lowQ ² andW<3 GeV. The soft or hadronic component is shown to dominate only at highW>6 GeV for values ofQ ²≤10 GeV².     

Inelastic electron scattering from protons and deuterons at very low Q2

The total cross-section for production of hadrons by inelastic electron scattering at 3.2° from hydrogen and deuterium has been measured in the Q² range 0.015 GeV² to 0.1 GeV², at virtual photon energies ranging from 2 GeV to 8.5 GeV. The transition to photoproduction is observed to be smooth, the ratio σ_D/σ_H being about 1.85 in this range. No evidence is seen for a conjectured rapid Q²-dependence of this ratio at low Q².     

Evaluation of fully integrated γ v p → π+π− p cross sections in the resonance region at photon virtualities 5 < Q 2 < 12 GeV2

Evaluation of fully integrated double pion electroproduction cross sections of protons was carried out at 1.4 < W < 2.0 GeV, 5 < Q ² < 12 GeV². The cross-section evaluation was obtained from an approach based on extrapolation of the double pion component of inclusive structure functions F ₁ and F ₂ from photon virtualities Q ² < 5 GeV² towards 5 < Q ² < 12 GeV². Q ²-parameterization compatible with restrictions from the Operator Product Expansion was used to conduct the extrapolation. The results will be used to extract double pion electroproduction cross sections of protons in future experiments with the new CLAS12 detector.     

Phenomenology of the proton spin

We analyze the various inputs that go into computing the recently measured first moment of the proton spin structure functiong ₁ ^p (x). The basic inputs are the various valence and sea quark polarisations and the gluonic contribution coming through axial anomaly. We show that the quark model predictions for valence quark polarisations, suitably modified to accommodate Bjorken sum rule, are consistent with measured value of moment of the spin structure function.     

Spin-dependent parton distributions in polarized deep inelastic lepton nucleon scattering

We analyze the recently measured first moment Г ^p (Q ²) of the structure functiong ₁ ^p (x,Q ²) obtained in deep inelastic scattering of polarized electrons from polarized protons. It is shown that the recent experimental result Г ^p (〈Q ²〉?10 GeV²)? 0.113 implies a polarized strange quark sea whose total polarization Δs(μ²)??0.22 is comparable to Δμ(μ²)?0.74 and Δd(μ²)??0.50 already at a typically hadronic scale μ=0(1 GeV). Most remarkably, the total polarization due to quark distributions Δμ(μ²)+Δd(μ²)+Δs(μ²) practically vanishes which implies that the spin of the proton is carried by the gluons, ΔG(μ²), and/or the angular momentum of the partons. This surprising conjecture can be experimentally tested with heavy quark production in longitudinally polarized lepton-nucleon scattering. In particular the (real) photon-gluon fusion process γg→Q \(\bar Q\) provides a rather unique measure of ΔG(x,Q ²).